An iterative process that is used to solve flow dynamics is studied; a highway culvert and embankment system serves as an example. Time step criteria governing convergence of the iterative process is analyzed. The Lipschitz ratio is applied to calculate the controlling algebraic time step relationship. The time step for convergence is shown to vary with current inflow and antecedent storage. Parameters of the iterative process are calculated for the example by assuming nonlinear functional forms for stage storage and discharge storage relationships and by inferring the appropriate coefficients. Numerical results are presented for several extreme cases that bracket orifice and weir flow conditions. The approach should be applicable to other hydrologic systems such as small dams, catch basin flow, and retarding basins. As for the route or convolute question, which concerns the direct conversion of rainfall excess to watershed outflow, this analysis aids in the selection of a time increment for direct routing.